1
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Shvedov NR, Analoui S, Dafalias T, Bedell BL, Gardner TJ, Scott BB. In vivo imaging in transgenic songbirds reveals superdiffusive neuron migration in the adult brain. Cell Rep 2024; 43:113759. [PMID: 38345898 DOI: 10.1016/j.celrep.2024.113759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Revised: 12/01/2023] [Accepted: 01/23/2024] [Indexed: 03/02/2024] Open
Abstract
Neuron migration is a key phase of neurogenesis, critical for the assembly and function of neuronal circuits. In songbirds, this process continues throughout life, but how these newborn neurons disperse through the adult brain is unclear. We address this question using in vivo two-photon imaging in transgenic zebra finches that express GFP in young neurons and other cell types. In juvenile and adult birds, migratory cells are present at a high density, travel in all directions, and make frequent course changes. Notably, these dynamic migration patterns are well fit by a superdiffusive model. Simulations reveal that these superdiffusive dynamics are sufficient to disperse new neurons throughout the song nucleus HVC. These results suggest that superdiffusive migration may underlie the formation and maintenance of nuclear brain structures in the postnatal brain and indicate that transgenic songbirds are a useful resource for future studies into the mechanisms of adult neurogenesis.
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Affiliation(s)
- Naomi R Shvedov
- Graduate Program for Neuroscience, Boston University, Boston, MA 02215, USA
| | - Sina Analoui
- Department of Psychological and Brain Sciences, Boston University, Boston, MA 02215, USA
| | - Theresia Dafalias
- Graduate Program for Neuroscience, Boston University, Boston, MA 02215, USA
| | - Brooke L Bedell
- Department of Psychological and Brain Sciences, Boston University, Boston, MA 02215, USA
| | - Timothy J Gardner
- Phil and Penny Knight Campus for Accelerating Scientific Impact, University of Oregon, Eugene, OR 97403, USA
| | - Benjamin B Scott
- Department of Psychological and Brain Sciences, Boston University, Boston, MA 02215, USA; Neurophotonics Center, Photonics Center, and Center for Systems Neuroscience, Boston University, Boston, MA 02215, USA.
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2
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Millan E, Lavaud M, Amarouchene Y, Salez T. Numerical simulations of confined Brownian-yet-non-Gaussian motion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:24. [PMID: 37002415 DOI: 10.1140/epje/s10189-023-00281-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 03/20/2023] [Indexed: 06/19/2023]
Abstract
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.
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Affiliation(s)
- Elodie Millan
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France
| | - Maxime Lavaud
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France
| | | | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France.
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3
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Granek O, Kafri Y, Tailleur J. Anomalous Transport of Tracers in Active Baths. PHYSICAL REVIEW LETTERS 2022; 129:038001. [PMID: 35905354 DOI: 10.1103/physrevlett.129.038001] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Revised: 12/23/2021] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.
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Affiliation(s)
- Omer Granek
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yariv Kafri
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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4
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Poncet A, Grabsch A, Bénichou O, Illien P. Exact time dependence of the cumulants of a tracer position in a dense lattice gas. Phys Rev E 2022; 105:054139. [PMID: 35706275 DOI: 10.1103/physreve.105.054139] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/03/2022] [Indexed: 06/15/2023]
Abstract
We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant-generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position, a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk and covers the important situations of (1) a biased tracer, (2) comblike structures, and (3) d-dimensional situations.
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Affiliation(s)
- Alexis Poncet
- Univ. Lyon, ENS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, 69342 Lyon, France
| | - Aurélien Grabsch
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Physicochimie des Electrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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5
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Malgaretti P, Puertas AM, Pagonabarraga I. Active microrheology in corrugated channels: Comparison of thermal and colloidal baths. J Colloid Interface Sci 2022; 608:2694-2702. [PMID: 34802755 DOI: 10.1016/j.jcis.2021.10.193] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Revised: 10/29/2021] [Accepted: 10/31/2021] [Indexed: 11/19/2022]
Abstract
HYPOTHESIS The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhomogeneities induced by the walls. METHOD Colloidal suspension confined within model porous media are characterized by means of active microrheology where a net force is applied on a single colloid (tracer particle) whose transport properties are then studied. The trajectories provided by active microrheology are exploited to determine the local transport coefficients. In order to asses the role of the colloid-colloid interactions we compare the case of a tracer embedded in a colloidal suspension to the case of a tracer suspended in an ideal bath. FINDING Our results show that the friction coefficient increases and the passage time distribution widens upon increasing the corrugation of the channel. These features are obtained for a tracer suspended in a (thermalized) colloidal bath as well as for the case of an ideal thermal bath. These results highlight the relevance of the confinement on the transport and show a mild dependence on the colloidal/thermal bath. Finally, we rationalize our numerical results with a semi-analytical model. Interestingly, the predictions of the model are quantitatively reliable for mild external forces, hence providing a reliable tool for predicting the transport across porous materials.
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Affiliation(s)
- Paolo Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Cauer Str. 1, 91058 Erlangen, Germany; Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany; IV Institute for Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
| | - Antonio M Puertas
- Departamento de Física Aplicada, Universidad de Almería, 04.120 Almería, Spain
| | - Ignacio Pagonabarraga
- Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne (EPFL), Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland; Departament de Fisica de la Materia Condensada, Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Spain; UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
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6
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Rizkallah P, Sarracino A, Bénichou O, Illien P. Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment. PHYSICAL REVIEW LETTERS 2022; 128:038001. [PMID: 35119883 DOI: 10.1103/physrevlett.128.038001] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.
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Affiliation(s)
- Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Dipartimento di Ingegneria, Università della Campania "Luigi Vanvitelli", 81031 Aversa (CE), Italy
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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7
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Hartich D, Godec A. Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion. PHYSICAL REVIEW LETTERS 2021; 127:080601. [PMID: 34477441 DOI: 10.1103/physrevlett.127.080601] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.
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Affiliation(s)
- David Hartich
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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8
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Jain R, Ginot F, Berner J, Bechinger C, Krüger M. Two step micro-rheological behavior in a viscoelastic fluid. J Chem Phys 2021; 154:184904. [PMID: 34241016 DOI: 10.1063/5.0048320] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.
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Affiliation(s)
- Rohit Jain
- Institute for Theoretical Physics, Georg-August Universität Göttingen, 37073 Göttingen, Germany
| | - Félix Ginot
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Johannes Berner
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | | | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August Universität Göttingen, 37073 Göttingen, Germany
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9
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Janušonis S, Detering N, Metzler R, Vojta T. Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities. Front Comput Neurosci 2020; 14:56. [PMID: 32670042 PMCID: PMC7328445 DOI: 10.3389/fncom.2020.00056] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Accepted: 05/19/2020] [Indexed: 01/03/2023] Open
Abstract
All vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and vascular processes. Perturbations in the density of this matrix have been associated with a number of mental disorders, including autism and depression, but its self-organization and plasticity remain poorly understood. We introduce a model based on reflected Fractional Brownian Motion (FBM), a rigorously defined stochastic process, and show that it recapitulates some key features of regional serotonergic fiber densities. Specifically, we use supercomputing simulations to model fibers as FBM-paths in two-dimensional brain-like domains and demonstrate that the resultant steady state distributions approximate the fiber distributions in physical brain sections immunostained for the serotonin transporter (a marker for serotonergic axons in the adult brain). We suggest that this framework can support predictive descriptions and manipulations of the serotonergic matrix and that it can be further extended to incorporate the detailed physical properties of the fibers and their environment.
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Affiliation(s)
- Skirmantas Janušonis
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, Santa Barbara, CA, United States
| | - Nils Detering
- Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA, United States
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | - Thomas Vojta
- Department of Physics, Missouri University of Science and Technology, Rolla, MO, United States
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10
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Akimoto T, Saito K. Trace of anomalous diffusion in a biased quenched trap model. Phys Rev E 2020; 101:042133. [PMID: 32422836 DOI: 10.1103/physreve.101.042133] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Accepted: 04/07/2020] [Indexed: 06/11/2023]
Abstract
Diffusion in a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drifts or the diffusion coefficients remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes 0 when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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11
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Valov A, Avetisov V, Nechaev S, Oshanin G. Field-driven tracer diffusion through curved bottlenecks: fine structure of first passage events. Phys Chem Chem Phys 2020; 22:18414-18422. [DOI: 10.1039/d0cp03162c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary.
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Affiliation(s)
- A. Valov
- N. N. Semenov Institute of Chemical Physics RAS
- 119991 Moscow
- Russia
| | - V. Avetisov
- N. N. Semenov Institute of Chemical Physics RAS
- 119991 Moscow
- Russia
| | - S. Nechaev
- Interdisciplinary Scientific Center Poncelet (CNRS UMI 2615)
- 119002 Moscow
- Russia
- P. N. Lebedev Physical Institute RAS
- 119991 Moscow
| | - G. Oshanin
- Sorbonne Université
- CNRS
- Laboratoire de Physique Théorique de la Matière Condensée
- LPTMC (UMR CNRS 7600)
- 75252 Paris
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12
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Şenbil N, Gruber M, Zhang C, Fuchs M, Scheffold F. Observation of Strongly Heterogeneous Dynamics at the Depinning Transition in a Colloidal Glass. PHYSICAL REVIEW LETTERS 2019; 122:108002. [PMID: 30932679 DOI: 10.1103/physrevlett.122.108002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Revised: 12/06/2018] [Indexed: 06/09/2023]
Abstract
We study experimentally the origin of heterogeneous dynamics in strongly driven glass-forming systems. Thereto, we apply a well-defined force with a laser line trap on individual colloidal polystyrene probe particles seeded in an emulsion glass composed of droplets of the same size. Fluid and glass states can be probed. We monitor the trajectories of the probe and measure displacements and their distributions. Our experiments reveal intermittent dynamics around a depinning transition at a threshold force. For smaller forces, linear response connects mean displacement, and quiescent mean squared displacement. Mode coupling theory calculations rationalize the observations.
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Affiliation(s)
- Nesrin Şenbil
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Markus Gruber
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Chi Zhang
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Frank Scheffold
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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13
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Korabel N, Waigh TA, Fedotov S, Allan VJ. Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate. PLoS One 2018; 13:e0207436. [PMID: 30475848 PMCID: PMC6261056 DOI: 10.1371/journal.pone.0207436] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2018] [Accepted: 10/31/2018] [Indexed: 11/19/2022] Open
Abstract
Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental trajectories of organelles inside a living cell and propose a mathematical model that describes the previously reported transition from sub-diffusive to super-diffusive motion. In order to explain super-diffusive behaviour at long times, we introduce non-Markovian detachment kinetics of the cargo: the rate of detachment is inversely proportional to the time since the last attachment. Recently, we observed the non-Markovian detachment rate experimentally in eukaryotic cells. Here we further discuss different scenarios of how this effective non-Markovian detachment rate could arise. The non-Markovian model is successful in simultaneously describing the time averaged variance (the time averaged mean squared displacement corrected for directed motion), the mean first passage time of trajectories and the multiple peaks observed in the distributions of cargo velocities. We argue that non-Markovian kinetics could be biologically beneficial compared to the Markovian kinetics commonly used for modelling, by increasing the average distance the cargoes travel when a microtubule is blocked by other filaments. In turn, sub-diffusion allows cargoes to reach neighbouring filaments with higher probability, which promotes active motion along the microtubules.
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Affiliation(s)
- Nickolay Korabel
- School of Mathematics, University of Manchester, Manchester, United Kingdom
- * E-mail:
| | - Thomas A. Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- The Photon Science Institute, University of Manchester, Manchester, United Kingdom
| | - Sergei Fedotov
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Viki J. Allan
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, Manchester, United Kingdom
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14
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Tracer diffusion in crowded narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:443001. [PMID: 30211693 DOI: 10.1088/1361-648x/aae13a] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.
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Affiliation(s)
- O Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 4 Place Jussieu, 75252 Paris Cedex 05, France
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15
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Puertas AM, Malgaretti P, Pagonabarraga I. Active microrheology in corrugated channels. J Chem Phys 2018; 149:174908. [DOI: 10.1063/1.5048343] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Antonio M. Puertas
- Department of Applied Physics, Universidad de Almería, 04120 Almería, Spain
| | - Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
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16
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Hou R, Cherstvy AG, Metzler R, Akimoto T. Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing. Phys Chem Chem Phys 2018; 20:20827-20848. [PMID: 30066003 DOI: 10.1039/c8cp01863d] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.
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Affiliation(s)
- Ru Hou
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
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17
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Akimoto T, Cherstvy AG, Metzler R. Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks. Phys Rev E 2018; 98:022105. [PMID: 30253516 DOI: 10.1103/physreve.98.022105] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2018] [Indexed: 06/08/2023]
Abstract
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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18
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Poncet A, Bénichou O, Démery V, Oshanin G. N-tag probability law of the symmetric exclusion process. Phys Rev E 2018; 97:062119. [PMID: 30011439 DOI: 10.1103/physreve.97.062119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Indexed: 11/07/2022]
Abstract
The symmetric exclusion process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognized qualitatively for a long time, up to now there has been no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically its large-time limit for an arbitrary density of particles, and its full dynamics in the high-density limit. In this limit, we obtain the time-dependent large deviation function of the problem and unveil a universal scaling form shared by the cumulants.
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Affiliation(s)
- Alexis Poncet
- LPTMC, CNRS/Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
| | - Olivier Bénichou
- LPTMC, CNRS/Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
| | - Vincent Démery
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, Paris, France.,Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Gleb Oshanin
- LPTMC, CNRS/Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
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19
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Cecconi F, Puglisi A, Sarracino A, Vulpiani A. Anomalous mobility of a driven active particle in a steady laminar flow. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:264002. [PMID: 29762125 DOI: 10.1088/1361-648x/aac4f0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale [Formula: see text]. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ([Formula: see text]) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite [Formula: see text] a more complex force-velocity relation can be observed.
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Affiliation(s)
- F Cecconi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
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20
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Illien P, Bénichou O, Oshanin G, Sarracino A, Voituriez R. Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment. PHYSICAL REVIEW LETTERS 2018; 120:200606. [PMID: 29864325 DOI: 10.1103/physrevlett.120.200606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 01/02/2018] [Indexed: 06/08/2023]
Abstract
We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.
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Affiliation(s)
- Pierre Illien
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
| | - Gleb Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185 Rome, Italy
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
- Laboratoire Jean Perrin, CNRS UMR 8237, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
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21
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Huveneers F. Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment. Phys Rev E 2018; 97:042116. [PMID: 29758602 DOI: 10.1103/physreve.97.042116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Indexed: 11/07/2022]
Abstract
We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D. We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.
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Affiliation(s)
- François Huveneers
- Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE, 75016 Paris, France
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22
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Bertrand T, Zhao Y, Bénichou O, Tailleur J, Voituriez R. Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments. PHYSICAL REVIEW LETTERS 2018; 120:198103. [PMID: 29799236 DOI: 10.1103/physrevlett.120.198103] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Revised: 02/18/2018] [Indexed: 06/08/2023]
Abstract
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.
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Affiliation(s)
- Thibault Bertrand
- Laboratoire Jean Perrin, UMR 8237 CNRS, Sorbonne Université, 75005 Paris, France
| | - Yongfeng Zhao
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, 75205 Paris, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS, Sorbonne Université, 75005 Paris, France
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, 75205 Paris, France
| | - Raphaël Voituriez
- Laboratoire Jean Perrin, UMR 8237 CNRS, Sorbonne Université, 75005 Paris, France
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS, Sorbonne Université, 75005 Paris, France
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23
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Leitmann S, Schwab T, Franosch T. Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas. Phys Rev E 2018; 97:022101. [PMID: 29548093 DOI: 10.1103/physreve.97.022101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2017] [Indexed: 11/07/2022]
Abstract
We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Schwab
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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24
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Berner J, Müller B, Gomez-Solano JR, Krüger M, Bechinger C. Oscillating modes of driven colloids in overdamped systems. Nat Commun 2018. [PMID: 29519999 PMCID: PMC5843593 DOI: 10.1038/s41467-018-03345-2] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
Microscopic colloidal particles suspended in liquids are a prominent example of an overdamped system where viscous forces dominate over inertial effects. Frequently, colloids are used as sensitive probes, e.g., in biophysical applications from which molecular forces are inferred. The interpretation of such experiments rests on the assumption that, even when the particles are driven, the liquid remains in equilibrium. Here we experimentally demonstrate that this is not valid for particles in viscoelastic fluids. Even at small driving forces, we observe particle oscillations with several tens of seconds. They are attributed to non-equilibrium fluctuations of the fluid being excited by the particle’s motion. The oscillatory dynamics is in quantitative agreement with an overdamped Langevin equation with negative friction-memory term being equivalent to a stochastically driven underdamped oscillator. Such oscillatory modes are expected to widen the use of colloids as model systems but must also be considered in colloidal probe experiments. The motion of microparticles suspended in liquids is assumed to be dominated by viscous forces. Here, Berner et al. challenge this consensus by observing underdamped particle oscillations in a viscoelastic fluid and attributing it to the non-equilibrium fluctuations of liquid excited by particles.
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Affiliation(s)
- Johannes Berner
- 2. Physikalisches Institut, Universität Stuttgart, D-70569, Stuttgart, Germany.,Fachbereich Physik, Universität Konstanz, D-78464, Konstanz, Germany
| | - Boris Müller
- Institut für Theoretische Physik IV, Universität Stuttgart, D-70569, Stuttgart, Germany.,Max-Planck-Institut für Intelligente Systeme, D-70569, Stuttgart, Germany
| | - Juan Ruben Gomez-Solano
- 2. Physikalisches Institut, Universität Stuttgart, D-70569, Stuttgart, Germany.,Fachbereich Physik, Universität Konstanz, D-78464, Konstanz, Germany
| | - Matthias Krüger
- Institut für Theoretische Physik IV, Universität Stuttgart, D-70569, Stuttgart, Germany.,Max-Planck-Institut für Intelligente Systeme, D-70569, Stuttgart, Germany.,Universität Göttingen, Institut für Theoretische Physik, D-37077, Göttingen, Germany
| | - Clemens Bechinger
- 2. Physikalisches Institut, Universität Stuttgart, D-70569, Stuttgart, Germany. .,Fachbereich Physik, Universität Konstanz, D-78464, Konstanz, Germany. .,Max-Planck-Institut für Intelligente Systeme, D-70569, Stuttgart, Germany.
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25
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Nizkaya TV, Asmolov ES, Vinogradova OI. Advective superdiffusion in superhydrophobic microchannels. Phys Rev E 2018; 96:033109. [PMID: 29346940 DOI: 10.1103/physreve.96.033109] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Indexed: 11/07/2022]
Abstract
We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can induce an advective superdiffusion, which strongly enhances dispersion of particles compared to a normal diffusion, and that maximal cross-sectional spreading corresponds to a crossover between its subballistic and superballistic regimes. This allows us to argue that an advective superdiffusion can be used for boosting dispersion of particles at smaller Péclet numbers compared to known concepts of passive microfluidic mixing. This implies that our superdiffusion scenario allows one efficient mixing of much smaller particles or using much thinner microchannels than methods, which are currently being exploited.
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Affiliation(s)
- Tatiana V Nizkaya
- A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Science, 31 Leninsky Prospect, 119071 Moscow, Russia
| | - Evgeny S Asmolov
- A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Science, 31 Leninsky Prospect, 119071 Moscow, Russia.,Institute of Mechanics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Olga I Vinogradova
- A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Science, 31 Leninsky Prospect, 119071 Moscow, Russia.,Department of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia.,DWI - Leibniz Institute for Interactive Materials, Forckenbeckstr. 50, 52056 Aachen, Germany
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26
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Abstract
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation, t→t/Λ^{1/α}, for a transient process in the subdiffusive regime is sufficient for asymptotic mapping. An exact form of the constant Λ^{1/α} is established. A disorder averaged position probability density function for a quenched trap model is obtained, and analytic expressions for the diffusion coefficient and drift are provided.
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Affiliation(s)
- Stanislav Burov
- Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel
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27
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Vasilyev OA, Bénichou O, Mejía-Monasterio C, Weeks ER, Oshanin G. Cooperative behavior of biased probes in crowded interacting systems. SOFT MATTER 2017; 13:7617-7624. [PMID: 28976526 DOI: 10.1039/c7sm00865a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We study, via extensive numerical simulations, dynamics of a crowded mixture of mutually interacting (with a short-range repulsive potential) colloidal particles immersed in a suspending solvent, acting as a heat bath. The mixture consists of a majority component - neutrally buoyant colloids subject to internal stimuli only, and a minority component - biased probes (BPs) also subject to a constant force. In such a system each of the BPs alters the distribution of the colloidal particles in its vicinity, driving their spatial distribution out of equilibrium. This induces effective long-range interactions and multi-tag correlations between the BPs, mediated by an out-of-equilibrium majority component, and prompts the BPs to move collectively assembling in clusters. We analyse the size-distribution of the self-assembling clusters in the steady-state, their specific force-velocity relations and also properties of the effective interactions emerging between the BPs.
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Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
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28
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Krüger M, Maes C. The modified Langevin description for probes in a nonlinear medium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:064004. [PMID: 28002047 DOI: 10.1088/1361-648x/29/6/064004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.
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Affiliation(s)
- Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, Stuttgart, Germany. Max Planck Institute for Intelligent Systems, Stuttgart, Germany
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29
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Leitmann S, Franosch T. Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas. PHYSICAL REVIEW LETTERS 2017; 118:018001. [PMID: 28106412 DOI: 10.1103/physrevlett.118.018001] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Indexed: 06/06/2023]
Abstract
We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient dynamics of the fluctuations of the tracer position along the direction of the force. The analytic result, exact in first order of the obstacle density and for arbitrarily strong driving, is compared to stochastic simulations. Upon strong driving, the fluctuations grow superdiffusively for intermediate times; however, they always become diffusive in the stationary state. The diffusion constant is nonanalytic for small driving and is enhanced by orders of magnitude by increasing the force.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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30
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Cividini J, Mukamel D, Posch HA. Driven tracers in narrow channels. Phys Rev E 2017; 95:012110. [PMID: 28208398 DOI: 10.1103/physreve.95.012110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Indexed: 06/06/2023]
Abstract
Steady-state properties of a driven tracer moving in a narrow two-dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one-dimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean-field theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.
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Affiliation(s)
- J Cividini
- Department of Physics of Complex Systems, Weizmann Institute of Science Rehovot, Israel 76100
| | - D Mukamel
- Department of Physics of Complex Systems, Weizmann Institute of Science Rehovot, Israel 76100
| | - H A Posch
- Computational Physics Group, Faculty of Physics, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria
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31
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Wulfert R, Seifert U, Speck T. Discontinuous thinning in active microrheology of soft complex matter. Phys Rev E 2016; 94:062610. [PMID: 28085442 DOI: 10.1103/physreve.94.062610] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Indexed: 06/06/2023]
Abstract
Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.
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Affiliation(s)
- R Wulfert
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
| | - U Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
| | - T Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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32
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Mahakrishnan S, Chakraborty S, Vijay A. Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory. J Phys Chem B 2016; 120:9608-20. [PMID: 27552086 DOI: 10.1021/acs.jpcb.6b06380] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example) as a dynamical cause of the perpetual molecular movement, which eventually manifests as an ordered motion, called the diffusion.
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Affiliation(s)
- Sathiya Mahakrishnan
- Department of Chemistry, Indian Institute of Technology Madras , Chennai 600036, India
| | - Subrata Chakraborty
- Department of Chemistry, Indian Institute of Technology Madras , Chennai 600036, India
| | - Amrendra Vijay
- Department of Chemistry, Indian Institute of Technology Madras , Chennai 600036, India
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33
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Gradenigo G, Bertin E, Biroli G. Field-induced superdiffusion and dynamical heterogeneity. Phys Rev E 2016; 93:060105. [PMID: 27415189 DOI: 10.1103/physreve.93.060105] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2016] [Indexed: 06/06/2023]
Abstract
By analyzing two kinetically constrained models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By numerical simulations and analytical arguments we demonstrate that the violation of the Stokes-Einstein relation and the field-induced superdiffusion observed during a long preasymptotic regime have the same physical origin: while a fraction of probes do not move, others jump repeatedly because they are close to local mobile regions. The anomalous fluctuations observed out of equilibrium in the presence of a pulling force ε,σ_{x}^{2}(t)=〈x_{ε}^{2}(t)〉-〈x_{ε}(t)〉^{2}∼t^{3/2}, which are accompanied by the asymptotic decay α_{ε}(t)∼t^{-1/2} of the non-Gaussian parameter from nontrivial values to zero, are due to the splitting of the probes population in the two (mobile and immobile) groups and to dynamical correlations, a mechanism expected to happen generically in supercooled liquids.
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Affiliation(s)
- Giacomo Gradenigo
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
| | - Eric Bertin
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
- CNRS, LIPHY, F-38000 Grenoble, France
| | - Giulio Biroli
- IPhT, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, Université Paris Diderot Sorbonne Paris-Cité, Sorbonne Universités UPMC Université Paris 06, CNRS, 24 rue Lhomond, 75005 Paris, France
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments. Phys Rev E 2016; 93:032128. [PMID: 27078313 DOI: 10.1103/physreve.93.032128] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2015] [Indexed: 06/05/2023]
Abstract
We study analytically the dynamics and the microstructural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active microrheology experiments, we consider here a minimal model comprising a geometrically confined lattice system (a two-dimensional striplike or a three-dimensional capillary-like system) populated by two types of hard-core particles with stochastic dynamics (a tracer particle driven by a constant external force and bath particles moving completely at random). Resorting to a decoupling scheme, which permits us to go beyond the linear-response approximation (Stokes regime) for arbitrary densities of the lattice gas particles, we determine the force-velocity relation for the tracer particle and the stationary density profiles of the host medium particles around it. These results are validated a posteriori by extensive numerical simulations for a wide range of parameters. Our theoretical analysis reveals two striking features: (a) We show that, under certain conditions, the terminal velocity of the driven tracer particle is a nonmonotonic function of the force, so in some parameter range the differential mobility becomes negative, and (b) the biased particle drives the whole system into a nonequilibrium steady state with a stationary particle density profile past the tracer, which decays exponentially, in sharp contrast with the behavior observed for unbounded lattices, where an algebraic decay is known to take place.
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Affiliation(s)
- O Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - P Illien
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - G Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - A Sarracino
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
| | - R Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Diffusion and Subdiffusion of Interacting Particles on Comblike Structures. PHYSICAL REVIEW LETTERS 2015; 115:220601. [PMID: 26650285 DOI: 10.1103/physrevlett.115.220601] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Indexed: 06/05/2023]
Abstract
We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only. In the limit of high density of the particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior ∼t^{3/4}. At longer times, a second regime is observed where standard diffusion is recovered, with a surprising nonanalytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like continuous time random walk description, we unveil a rich and complex scenario with several successive subdiffusive regimes, resulting from the coupling between the geometrical constraints of the comb lattice and particle interactions. In this case, remarkably, the presence of hard-core interactions asymptotically speeds up the TP motion along the backbone of the structure.
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Affiliation(s)
- O Bénichou
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France
| | - P Illien
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France
| | - G Oshanin
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France
| | - A Sarracino
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France
| | - R Voituriez
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France
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Reverey JF, Jeon JH, Bao H, Leippe M, Metzler R, Selhuber-Unkel C. Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii. Sci Rep 2015; 5:11690. [PMID: 26123798 PMCID: PMC5155589 DOI: 10.1038/srep11690] [Citation(s) in RCA: 84] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Accepted: 06/01/2015] [Indexed: 12/21/2022] Open
Abstract
Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.
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Affiliation(s)
- Julia F Reverey
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
| | - Jae-Hyung Jeon
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
| | - Han Bao
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
| | - Matthias Leippe
- Zoological Institute, Comparative Immunobiology, Christian-Albrechts-Universität zu Kiel, Olshausenstr.40, D-24098 Kiel, Germany
| | - Ralf Metzler
- 1] Institute of Physics &Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany [2] Department of Physics, Tampere University of Technology, FI-30101 Tampere, Finland
| | - Christine Selhuber-Unkel
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
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Zhang K, Tian X, Bian X, Li Y, Liu Y. An equation describing diffusivity of liquid atoms by magnetic confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:235104. [PMID: 25992587 DOI: 10.1088/0953-8984/27/23/235104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this work, we report an obvious low field-induced magnetic confinement effect on the diffusivity in binary metallic melts under a weak magnetic field. A quantitative description of this nontrivial dynamic behavior is given by a physical analytical model based on the Hall effect, which is in agreement with our experimental results. Meanwhile, a quadratic B dependence of the dynamic viscosity obtained in the same confined environment is observed. Our results show that one can effectively control the atomic diffusion process of metallic melts by the application of magnetic field. Meanwhile, this magnetic confinement effect at atomic scale should provide an important new ingredient to deeply understand the condensed matter physics under the external magnetic field.
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Affiliation(s)
- Kai Zhang
- Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, School of Materials Science and Engineering, Shandong University, Jingshi Road 17923, Jinan 250061, People's Republic of China
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Microscopic theory for negative differential mobility in crowded environments. PHYSICAL REVIEW LETTERS 2014; 113:268002. [PMID: 25615388 DOI: 10.1103/physrevlett.113.268002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of the obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.
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Affiliation(s)
- O Bénichou
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matiére Condensée, F-75005 Paris, France
| | - P Illien
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matiére Condensée, F-75005 Paris, France
| | - G Oshanin
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matiére Condensée, F-75005 Paris, France
| | - A Sarracino
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matiére Condensée, F-75005 Paris, France
| | - R Voituriez
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matiére Condensée, F-75005 Paris, France
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40
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Hegde C, Sabhapandit S, Dhar A. Universal large deviations for the tagged particle in single-file motion. PHYSICAL REVIEW LETTERS 2014; 113:120601. [PMID: 25279614 DOI: 10.1103/physrevlett.113.120601] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Indexed: 06/03/2023]
Abstract
We consider a gas of point particles moving in a one-dimensional channel with a hard-core interparticle interaction that prevents particle crossings--this is called single-file motion. Starting from equilibrium initial conditions we observe the motion of a tagged particle. It is well known that if the individual particle dynamics is diffusive, then the tagged particle motion is subdiffusive, while for ballistic particle dynamics, the tagged particle motion is diffusive. Here we compute the exact large deviation function for the tagged particle displacement and show that this is universal, independent of the individual dynamics.
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Affiliation(s)
| | | | - Abhishek Dhar
- International Centre for Theoretical Sciences, TIFR, Bangalore 560012, India
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41
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Lee AA, Kondrat S, Oshanin G, Kornyshev AA. Charging dynamics of supercapacitors with narrow cylindrical nanopores. NANOTECHNOLOGY 2014; 25:315401. [PMID: 25026503 DOI: 10.1088/0957-4484/25/31/315401] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a coarse-grained, continuum kinetic theory for charging supercapacitors with narrow cylindrical nanopores. The theory reveals that the occupancy of a nonpolarized pore and the energy barrier for ion-ion interdiffusion are the key issues controlling the different regimes of dynamic response. For 'ionophobic' pores, where the pore is empty at no applied voltage, charge density advances into the pore via diffusion-like dynamics. The mechanism of charging an 'ionophilic' pore is starkly different: for moderate ionophilicities, co-ions are expelled from the pore in a front-like manner, with significant 'congestion' at the pore entrance predicted for strong ionophilicity. We thus show that pore ionophilicity is detrimental to the speed of charging/discharging cycles, whereas making pores more ionophobic can substantially accelerate charging and cyclic recharging.
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Affiliation(s)
- Alpha A Lee
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK. Department of Chemistry, Faculty of Natural Sciences, Imperial College London, SW7 2AZ, UK
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42
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Illien P, Bénichou O, Oshanin G, Voituriez R. Velocity anomaly of a driven tracer in a confined crowded environment. PHYSICAL REVIEW LETTERS 2014; 113:030603. [PMID: 25083625 DOI: 10.1103/physrevlett.113.030603] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Indexed: 06/03/2023]
Abstract
We consider a discrete model in which a tracer performs a random walk biased by an external force, in a dense bath of particles performing symmetric random walks constrained by hard-core interactions. We reveal the emergence of a striking velocity anomaly in confined geometries: in quasi-1D systems such as stripes or capillaries, the velocity of the tracer displays a long-lived plateau before ultimately dropping to a lower value. We develop an analytical solution that quantitatively accounts for this intriguing behavior. Our analysis suggests that such a velocity anomaly could be a generic feature of driven dynamics in quasi-1D crowded systems.
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Affiliation(s)
- Pierre Illien
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France
| | - Gleb Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France and Laboratoire Jean Perrin, FRE 3231 CNRS /UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
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Metzler R, Jeon JH, Cherstvy AG, Barkai E. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys Chem Chem Phys 2014; 16:24128-64. [DOI: 10.1039/c4cp03465a] [Citation(s) in RCA: 1046] [Impact Index Per Article: 104.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
This Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data.
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Affiliation(s)
- Ralf Metzler
- Institute of Physics and Astronomy
- University of Potsdam
- Potsdam-Golm, Germany
- Physics Department
- Tampere University of Technology
| | - Jae-Hyung Jeon
- Physics Department
- Tampere University of Technology
- Tampere, Finland
- Korean Institute for Advanced Study (KIAS)
- Seoul, Republic of Korea
| | - Andrey G. Cherstvy
- Institute of Physics and Astronomy
- University of Potsdam
- Potsdam-Golm, Germany
| | - Eli Barkai
- Physics Department and Institute of Nanotechnology and Advanced Materials
- Bar-Ilan University
- Ramat Gan, Israel
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